A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that (i) She will buy it ? (ii) She will not buy it ?
Step-by-Step Solution
Key Concept: Use the classical definition of probability: $$P(E)=\frac{\text{Number of favourable outcomes}}{\text{Total number of equally likely outcomes}}.$$ Here the total number of pens is 144. The favourable outcomes for buying are the good pens, and for not buying are the defective pens.
1. Total number of pens \(N = 144\).
2. Number of defective pens \(D = 20\).
3. Number of good pens \(G = N - D = 144 - 20 = 124\).
4. Probability of buying the pen (pen is good):
$$P(\text{buy}) = \frac{\text{Number of good pens}}{\text{Total pens}} = \frac{124}{144} = \frac{31}{36}.$$
5. Probability of not buying the pen (pen is defective):
$$P(\text{not buy}) = \frac{\text{Number of defective pens}}{\text{Total pens}} = \frac{20}{144} = \frac{5}{36}.$$
6. Check: \(P(\text{buy}) + P(\text{not buy}) = \frac{31}{36} + \frac{5}{36} = 1\), which is consistent with the total probability rule.
Correct Answer: (i) \(\displaystyle \frac{31}{36}\)
(ii) \(\displaystyle \frac{5}{36}\)